Recently, solving the complex design optimization problems with design uncertainties has become an important but very challenging task in the communities of reliability-based design optimization (RBDO) and multidisciplinary design optimization (MDO). The MDO algorithms decompose the complex design problem into the hierarchical or nonhierarchical optimization structure and distribute the workloads to each discipline (or subproblem) in the decomposed structure. The coordination of the local responses is crucial for the success of finding the optimal design point. The problem complexity increases dramatically when the existence of the design uncertainties is not negligible. The RBDO algorithms perform the reliability analyses to evaluate the probabilities that the random variables violate the constraints. However, the required reliability analyses build up the degree of complexity. In this paper, the gradient-based transformation method (GTM) is utilized to reduce the complexity of the MDO problems by transforming the design space to multiple single-variate monotonic coordinates along the directions of the constraint gradients. The subsystem responses are found using the monotonicity principles (MP) and then coordinated for the new design points based on two general principles. To consider the design uncertainties, the probabilistic gradient-based transformation method (PGTM) is proposed to adapt the first-order probabilistic constraints from three different RBDO algorithms, including the chance constrained programming (CCP), reliability index approach (RIA), and performance measure approach (PMA), to the framework of the GTM. PGTM is efficient because only the sensitivity analyses and the reliability analyses require function evaluations (FE). The optimization processes of monotonicity analyses and the coordination procedures are free of function evaluations. Several mathematical and engineering examples show the PGTM is capable of finding the optimal solutions with desirable reliability levels.
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February 2013
Research-Article
Reliability-Based Multidisciplinary Design Optimization Using Probabilistic Gradient-Based Transformation Method
Po Ting Lin,
Po Ting Lin
1
Assistant Professor
Department of Mechanical Engineering,
Research and Development Center
for Microsystem Reliability,
Chungli City,
Taoyuan County,
e-mail: potinglin@cycu.edu.tw
Department of Mechanical Engineering,
Research and Development Center
for Microsystem Reliability,
Chung Yuan Christian University
,Chungli City,
Taoyuan County,
Taiwan
32023e-mail: potinglin@cycu.edu.tw
1Corresponding author.
Search for other works by this author on:
Hae Chang Gea
Hae Chang Gea
Professor
Department of Mechanical and
Aerospace Engineering,
Rutgers,
Piscataway, NJ 08854
e-mail: gea@rci.rutgers.edu
Department of Mechanical and
Aerospace Engineering,
Rutgers,
The State University of New Jersey
,Piscataway, NJ 08854
e-mail: gea@rci.rutgers.edu
Search for other works by this author on:
Po Ting Lin
Assistant Professor
Department of Mechanical Engineering,
Research and Development Center
for Microsystem Reliability,
Chungli City,
Taoyuan County,
e-mail: potinglin@cycu.edu.tw
Department of Mechanical Engineering,
Research and Development Center
for Microsystem Reliability,
Chung Yuan Christian University
,Chungli City,
Taoyuan County,
Taiwan
32023e-mail: potinglin@cycu.edu.tw
Hae Chang Gea
Professor
Department of Mechanical and
Aerospace Engineering,
Rutgers,
Piscataway, NJ 08854
e-mail: gea@rci.rutgers.edu
Department of Mechanical and
Aerospace Engineering,
Rutgers,
The State University of New Jersey
,Piscataway, NJ 08854
e-mail: gea@rci.rutgers.edu
1Corresponding author.
Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received January 16, 2012; final manuscript received October 19, 2012; published online December 10, 2012. Assoc. Editor: Wei Chen.
J. Mech. Des. Feb 2013, 135(2): 021001 (12 pages)
Published Online: December 10, 2012
Article history
Received:
January 16, 2012
Revision Received:
October 19, 2012
Citation
Ting Lin, P., and Chang Gea, H. (December 10, 2012). "Reliability-Based Multidisciplinary Design Optimization Using Probabilistic Gradient-Based Transformation Method." ASME. J. Mech. Des. February 2013; 135(2): 021001. https://doi.org/10.1115/1.4023025
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